A power meter will show you the amount of power being drawn at the moment you look at the meter. It is like looking at the speedometer of your car at various times during a trip between two cities. It will show you the speed you are making at that moment, but will not help you know how long the trip will take or the average speed you will achieve during the trip. If you drive at a constant speed of 60 MPH, then your average speed during the trip will be 60 MPH. No surprise there. But if you are slowing down and speeding up in response to traffic conditions, then looking at your speedometer at any given moment will not give you a number that represents your average speed.
Your formula that uses KWH will tell you the average power (similar to the average speed you are driving) during the period of time for which the KWH value was measured. It is essentially the same thing as measuring the total distance you travelled between the two cities, and dividing that by the amount of time the trip took you.
So there really is no matter of an "error" between the two things you mention. They are simply different things, and there is no reason to expect them to give you the same result.